I think they're all the same company, in fact. I think it's all Paul van Aacken's company. They started with just Aackosoft. Then they seem to have named the programming team "The ByteBusters" at some point. The release label is mostly "Eaglesoft". Some newer titles seem to have been programmed by free lancers (like "Double Brain"

and got released under "Methodic Solutions". In the Methodic Solutions loading screen you see a few of the guys, one is named Paul, I guess that is Paul van Aacken.
Around 1988 when "The Games Collection" came out, they rereleased several older games (some had quite a touch up or slightly different names) under the name of "Eurosoft". Distribution by "Premium III Software Distribution"... These games were also the versions in The Games Collection, which was also under Eurosoft/Premium III.
All of this is quite confusing and a pain for Generation MSX maintainers like me... But still, AFAIK, it's all one and the same company.
Less known: Aackosoft International also released some stuff in Japan (e.g. Break-In, Kick-It), together with HAL e.g.) and in the beginning there's also Aackosoft Edusystems, with educational software.
Note: the above can contain errors, it's just my theory on how things worked (by looking what they released and stuff). I have no sources that can confirm this... Who has??